Let (Xn)EN be a sequence of i.i.d. random variables with E[X] = = R and Var[X] = (0, ). We define We define Xn = 1 n n 1 X (sample mean), S2 n 1 (X; - Xn) (sample variance). i=1 i=1 Assume furthermore that exists. Show that n n n i=1 = E[(X1 )4] (04,) (the centered fourth moment of X1) d n ()' N (0, (c) ). Conclude that n (S 2 - 0) d N(0, (c) ). nX